Question

How much thermal energy is needed to raise the temperature of a 3.0-kg copper block from \(25.0^{\circ} \mathrm{C}\) to \(125^{\circ} \mathrm{C} ?\) a) \(116 \mathrm{~kJ}\) b) \(278 \mathrm{~kJ}\) c) \(421 \mathrm{~kJ}\) d) \(576 \mathrm{~kJ}\) e) \(761 \mathrm{k}\)

Short answer

Short Answer: The amount of thermal energy needed is approximately 116 kJ.

Step-by-step solution

Identifying the given information

The mass of the copper block (m) is 3.0 kg. The initial temperature (T1) is \(25.0^{\circ} \mathrm{C}\). The final temperature (T2) is \(125^{\circ} \mathrm{C}\).

Calculate the change in temperature

ΔT = T2 - T1 ΔT = \(125^{\circ} \mathrm{C}\) - \(25.0^{\circ} \mathrm{C}\) ΔT = \(100^{\circ} \mathrm{C}\)

Determine the specific heat capacity of copper

The specific heat capacity (c) of copper is \(0.385 \frac{\mathrm{J}}{\mathrm{g} \cdot^{\circ}\mathrm{C}}\). Since the mass is given in kg, we'll need to convert the specific heat capacity to \(\frac{\mathrm{J}}{\mathrm{kg} \cdot^{\circ}\mathrm{C}}\). 1 kg = 1000 g Specific heat capacity of copper (c) = \(0.385 \frac{\mathrm{J}}{\mathrm{g} \cdot^{\circ}\mathrm{C}} \times \frac{1000 \mathrm{g}}{1 \mathrm{kg}} = 385 \frac{\mathrm{J}}{\mathrm{kg} \cdot^{\circ}\mathrm{C}}\).

Calculate the thermal energy required

We will use the formula for thermal energy, which is Q = mcΔT. Q = (3.0 kg) × (385 \(\frac{\mathrm{J}}{\mathrm{kg} \cdot^{\circ}\mathrm{C}}\)) × (100 \(^{\circ}\mathrm{C}\)) Q = 115500 J

Convert the result to kJ and compare to answer choices

Convert the result from J to kJ by dividing by 1000. Q = 115500 J ÷ 1000 Q = 115.5 kJ The closest answer choice to our calculated result is a) 116 kJ.